The specifics for the studies may differ but the focus for these types is on change over time or age-related differences. In cross-sectional studies the data is collected at one time but for different ages. For example, this study could compare 4-, 6-, and 8-year-olds to see how they differ in terms of the impact of yoga on self-esteem.
In contrast, a longitudinal study would follow a single group over a period of time. For example, following a group of 4-year-olds who practice yoga for four years, measuring their self-esteem at age 4, 6, and 8. These developmental studies allow us to look at age-related differences, as well as how the impact of a variable may change over time.